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Questions and Answers
Which statement best describes a set?
Which statement best describes a set?
- An ordered list of elements, where repetition is allowed.
- A random assortment of numbers without any structure.
- A collection of objects considered as a whole. (correct)
- A fixed sequence of items that must remain unchanged.
In set notation, how is the set of natural numbers typically represented?
In set notation, how is the set of natural numbers typically represented?
- N = {x | x > 0}
- N = {1, 2, 3, ...} (correct)
- N = {0, 1, 2, ...}
- N = {1, 1, 2, 3, 4, 5}
Which of the following is not a characteristic of a set?
Which of the following is not a characteristic of a set?
- Order of elements does not matter.
- A set can contain different types of elements.
- A set can be empty.
- Elements can repeat in a set. (correct)
What is the cardinality of a set?
What is the cardinality of a set?
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Which of the following represents a subset?
Which of the following represents a subset?
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Study Notes
Sets in Mathematics
- A set is a well-defined collection of distinct objects.
- Sets are typically represented by capital letters.
- The natural numbers are represented by the symbol â„•.
Set Notation
- The natural numbers are typically represented in set notation as: â„• = {1, 2, 3, ...}.
Characteristics of Sets
- Sets are well-defined: Each object in a set is clearly identifiable.
- Sets contain distinct objects: No object can appear more than once in a set.
- The order of objects in a set is not important.
Cardinality of a Set
- The cardinality of a set is the number of elements in the set.
- It is denoted by |S|, where S is the set.
Subsets
- A subset is a set where all elements are also contained within another set.
- A subset of set A is represented by the symbol A ⊆ B.
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